Line Paths Alternative?
Instead of parenting your object to the path, you can use a "follow path" constraint. 

Set the offset value to the frame number you want your object to follow the path and in the same frame set a keyframe to put the object in the 0,0,0 location. Push the button animate path in the constraint tab, and set the timing of the path in the curve's property panel, "path animation" tab. 

A the end of the animation set some keyframes to animate the influence of the follow path constraint, so you will be able to freely animate your object.